To calculate Whitham modulation equations, either a Lagrangian for the governing equations, or conservation
laws for these equations can be used, or a mixture of both [1]}, [2]}, [3]}. The use of Lagrangians has resulted
in this method of analysing slowly varying modulated wavetrains also being termed the method of averaged Lagrangians. As for
the determination of the modulation equations for the KdV equation, it was found that a combination of
an averaged Lagrangian and conservation equations is optimal [1]}, [3]}. The nematic equations in shallow
water form (REF )–() have the Lagrangian
\(L = -2\rho \phi _{z} - \frac{1}{4} \frac{\rho _{x}^{2}}{\rho } - \rho \phi _{x}^{2} - 4\rho \theta + \nu \theta _{x}^{2} + 2q\theta ^{2}.\) 
